diff --git a/CMakeLists.txt b/CMakeLists.txt index c7161317de..74e1a840a0 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -284,6 +284,9 @@ project (Jerry CXX C ASM) set(INCLUDE_LIBC_INTERFACE ${EXTERNAL_LIBC_INTERFACE}) endif() + # Jerry's fdlibm + add_subdirectory(third-party/fdlibm) + # Jerry's Core add_subdirectory(jerry-core) @@ -304,6 +307,7 @@ project (Jerry CXX C ASM) set(CORE_TARGET_NAME ${CORE_TARGET_NAME}${MODIFIER_SUFFIX_${MODIFIER}}) endforeach() + set(FDLIBM_TARGET_NAME ${CORE_TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB}) set(CORE_TARGET_NAME ${CORE_TARGET_NAME}.jerry-core) set(DEFINES_JERRY ) @@ -327,8 +331,9 @@ project (Jerry CXX C ASM) target_compile_definitions(${TARGET_NAME} PRIVATE ${DEFINES_JERRY}) target_include_directories(${TARGET_NAME} PRIVATE ${INCLUDE_CORE_INTERFACE}) target_include_directories(${TARGET_NAME} SYSTEM PRIVATE ${INCLUDE_LIBC_INTERFACE}) + target_link_libraries(${TARGET_NAME} ${PLUGINS_TARGET_NAME} ${CORE_TARGET_NAME} ${LIBC_TARGET_NAME} - ${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh) + ${FDLIBM_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh) add_cppcheck_target(${TARGET_NAME}) @@ -401,6 +406,7 @@ project (Jerry CXX C ASM) set(TARGET_NAME unit_${TARGET_NAME}) set(CORE_TARGET_NAME unittests.jerry-core) + set(FDLIBM_TARGET_NAME unittests.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB}) add_executable(${TARGET_NAME} ${SOURCE_UNIT_TEST_MAIN}) set_property(TARGET ${TARGET_NAME} @@ -408,7 +414,7 @@ project (Jerry CXX C ASM) set_property(TARGET ${TARGET_NAME} PROPERTY LINK_FLAGS "${COMPILE_FLAGS_JERRY} ${CXX_FLAGS_JERRY} ${FLAGS_COMMON_UNITTESTS} ${LINKER_FLAGS_COMMON}") target_include_directories(${TARGET_NAME} PRIVATE ${INCLUDE_CORE_INTERFACE}) - target_link_libraries(${TARGET_NAME} ${CORE_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libc + target_link_libraries(${TARGET_NAME} ${CORE_TARGET_NAME} ${FDLIBM_TARGET_NAME} ${PREFIX_IMPORTED_LIB}libc ${PREFIX_IMPORTED_LIB}libgcc ${PREFIX_IMPORTED_LIB}libgcc_eh) add_cppcheck_target(${TARGET_NAME}) diff --git a/Makefile b/Makefile index eec8d7fd86..1e3761f879 100644 --- a/Makefile +++ b/Makefile @@ -200,6 +200,8 @@ $(BUILD_ALL)_native: $(BUILD_DIRS_NATIVE) @ mkdir -p $(OUT_DIR)/$@ @ $(MAKE) -C $(BUILD_DIR)/native jerry-libc-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \ (echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;) + @ $(MAKE) -C $(BUILD_DIR)/native jerry-fdlibm-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \ + (echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;) @ $(MAKE) -C $(BUILD_DIR)/native plugins-all VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \ (echo "Build failed. See $(OUT_DIR)/$@/make.log for details."; exit 1;) @ $(MAKE) -C $(BUILD_DIR)/native $(JERRY_LINUX_TARGETS) unittests VERBOSE=1 &>$(OUT_DIR)/$@/make.log || \ diff --git a/jerry-core/CMakeLists.txt b/jerry-core/CMakeLists.txt index 9caead6d25..b54c547980 100644 --- a/jerry-core/CMakeLists.txt +++ b/jerry-core/CMakeLists.txt @@ -152,6 +152,7 @@ project (JerryCore CXX C ASM) PROPERTY COMPILE_FLAGS "${COMPILE_FLAGS_JERRY} ${CXX_FLAGS_JERRY} ${FLAGS_COMMON_${BUILD_MODE}}") target_compile_definitions(${TARGET_NAME}.jerry-core PRIVATE ${DEFINES_JERRY}) target_include_directories(${TARGET_NAME}.jerry-core PRIVATE ${INCLUDE_CORE}) + target_include_directories(${TARGET_NAME}.jerry-core PRIVATE ${INCLUDE_FDLIBM}) target_include_directories(${TARGET_NAME}.jerry-core SYSTEM PRIVATE ${INCLUDE_LIBC_INTERFACE}) if("${BUILD_MODE}" STREQUAL "UNITTESTS") diff --git a/jerry-core/ecma/base/ecma-globals.h b/jerry-core/ecma/base/ecma-globals.h index 03e467cbc5..f78e9890a8 100644 --- a/jerry-core/ecma/base/ecma-globals.h +++ b/jerry-core/ecma/base/ecma-globals.h @@ -566,6 +566,7 @@ typedef uint16_t ecma_char_t; * Description of an ecma-number */ typedef float ecma_number_t; +#define DOUBLE_TO_ECMA_NUMBER_T(value) static_cast (value) /** * Maximum number of significant digits that ecma-number can store @@ -576,6 +577,7 @@ typedef float ecma_number_t; * Description of an ecma-number */ typedef double ecma_number_t; +#define DOUBLE_TO_ECMA_NUMBER_T(value) value /** * Maximum number of significant digits that ecma-number can store diff --git a/jerry-core/ecma/builtin-objects/ecma-builtin-math.cpp b/jerry-core/ecma/builtin-objects/ecma-builtin-math.cpp index 3e019179c2..7b472442aa 100644 --- a/jerry-core/ecma/builtin-objects/ecma-builtin-math.cpp +++ b/jerry-core/ecma/builtin-objects/ecma-builtin-math.cpp @@ -1,4 +1,5 @@ /* Copyright 2014-2015 Samsung Electronics Co., Ltd. + * Copyright 2015 University of Szeged. * * Licensed under the Apache License, Version 2.0 (the "License"); * you may not use this file except in compliance with the License. @@ -25,6 +26,7 @@ #include "ecma-objects-general.h" #include "ecma-try-catch-macro.h" #include "jrt.h" +#include "fdlibm-math.h" #ifndef CONFIG_ECMA_COMPACT_PROFILE_DISABLE_MATH_BUILTIN @@ -64,14 +66,7 @@ ecma_builtin_math_object_abs (ecma_value_t this_arg __attr_unused___, /**< 'this ecma_number_t *num_p = ecma_alloc_number (); - if (ecma_number_is_nan (arg_num)) - { - *num_p = arg_num; - } - else - { - *num_p = ecma_number_abs (arg_num); - } + *num_p = DOUBLE_TO_ECMA_NUMBER_T (fabs (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); @@ -90,10 +85,20 @@ ecma_builtin_math_object_abs (ecma_value_t this_arg __attr_unused___, /**< 'this * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_acos (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_acos (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (acos (arg_num)); + + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_acos */ /** @@ -106,10 +111,20 @@ ecma_builtin_math_object_acos (ecma_value_t this_arg, /**< 'this' argument */ * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_asin (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_asin (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (asin (arg_num)); + + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_asin */ /** @@ -122,10 +137,20 @@ ecma_builtin_math_object_asin (ecma_value_t this_arg, /**< 'this' argument */ * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_atan (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_atan (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (atan (arg_num)); + + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_atan */ /** @@ -138,11 +163,23 @@ ecma_builtin_math_object_atan (ecma_value_t this_arg, /**< 'this' argument */ * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_atan2 (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_atan2 (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg1, /**< first routine's argument */ ecma_value_t arg2) /**< second routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg1, arg2); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (x, arg1, ret_value); + ECMA_OP_TO_NUMBER_TRY_CATCH (y, arg2, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (atan2 (x, y)); + + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (y); + ECMA_OP_TO_NUMBER_FINALIZE (x); + return ret_value; } /* ecma_builtin_math_object_atan2 */ /** @@ -155,10 +192,19 @@ ecma_builtin_math_object_atan2 (ecma_value_t this_arg, /**< 'this' argument */ * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_ceil (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_ceil (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (ceil (arg_num)); + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_ceil */ /** @@ -179,53 +225,10 @@ ecma_builtin_math_object_cos (ecma_value_t this_arg __attr_unused___, /**< 'this ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); ecma_number_t *num_p = ecma_alloc_number (); - - if (ecma_number_is_nan (arg_num) - || ecma_number_is_infinity (arg_num)) - { - *num_p = ecma_number_make_nan (); - } - else if (ecma_number_is_zero (arg_num)) - { - *num_p = ECMA_NUMBER_ONE; - } - else - { - /* Taylor series of cos (x) around x = 0 is 1 - x^2/2! + x^4/4! - x^6/6! + ... */ - - ecma_number_t x = ecma_op_number_remainder (arg_num, 2 * ECMA_NUMBER_PI); - ecma_number_t neg_sqr_x = ecma_number_negate (ecma_number_multiply (x, x)); - - ecma_number_t sum = ECMA_NUMBER_ZERO; - ecma_number_t next_addendum = ECMA_NUMBER_ONE; - ecma_number_t next_factorial_factor = ECMA_NUMBER_ZERO; - - ecma_number_t diff = ecma_number_make_infinity (false); - - while ((ecma_number_is_zero (sum) && !ecma_number_is_zero (diff)) - || (!ecma_number_is_zero (sum) - && ecma_number_abs (ecma_number_divide (diff, sum)) > ecma_number_relative_eps)) - { - ecma_number_t next_sum = ecma_number_add (sum, next_addendum); - - next_addendum = ecma_number_multiply (next_addendum, neg_sqr_x); - next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE); - next_addendum = ecma_number_divide (next_addendum, next_factorial_factor); - next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE); - next_addendum = ecma_number_divide (next_addendum, next_factorial_factor); - - diff = ecma_number_abs (ecma_number_substract (sum, next_sum)); - - sum = next_sum; - } - - *num_p = sum; - } - + *num_p = DOUBLE_TO_ECMA_NUMBER_T (cos (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); ECMA_OP_TO_NUMBER_FINALIZE (arg_num); - return ret_value; } /* ecma_builtin_math_object_cos */ @@ -248,29 +251,7 @@ ecma_builtin_math_object_exp (ecma_value_t this_arg __attr_unused___, /**< 'this ecma_number_t *num_p = ecma_alloc_number (); - if (ecma_number_is_nan (arg_num)) - { - *num_p = arg_num; - } - else if (ecma_number_is_zero (arg_num)) - { - *num_p = ECMA_NUMBER_ONE; - } - else if (ecma_number_is_infinity (arg_num)) - { - if (ecma_number_is_negative (arg_num)) - { - *num_p = ECMA_NUMBER_ZERO; - } - else - { - *num_p = arg_num; - } - } - else - { - *num_p = ecma_number_exp (arg_num); - } + *num_p = DOUBLE_TO_ECMA_NUMBER_T (exp (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); @@ -289,10 +270,19 @@ ecma_builtin_math_object_exp (ecma_value_t this_arg __attr_unused___, /**< 'this * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_floor (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_floor (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (floor (arg_num)); + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_floor */ /** @@ -314,26 +304,7 @@ ecma_builtin_math_object_log (ecma_value_t this_arg __attr_unused___, /**< 'this ecma_number_t *num_p = ecma_alloc_number (); - if (ecma_number_is_nan (arg_num)) - { - *num_p = arg_num; - } - else if (ecma_number_is_zero (arg_num)) - { - *num_p = ecma_number_make_infinity (true); - } - else if (ecma_number_is_negative (arg_num)) - { - *num_p = ecma_number_make_nan (); - } - else if (ecma_number_is_infinity (arg_num)) - { - *num_p = arg_num; - } - else - { - *num_p = ecma_number_ln (arg_num); - } + *num_p = DOUBLE_TO_ECMA_NUMBER_T (log (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); @@ -536,212 +507,7 @@ ecma_builtin_math_object_pow (ecma_value_t this_arg __attr_unused___, /**< 'this ECMA_OP_TO_NUMBER_TRY_CATCH (y, arg2, ret_value); ecma_number_t *num_p = ecma_alloc_number (); - - if (ecma_number_is_nan (y) - || (ecma_number_is_nan (x) - && !ecma_number_is_zero (y))) - { - *num_p = ecma_number_make_nan (); - } - else if (ecma_number_is_zero (y)) - { - *num_p = ECMA_NUMBER_ONE; - } - else if (ecma_number_is_infinity (y)) - { - const ecma_number_t x_abs = ecma_number_abs (x); - - if (x_abs == ECMA_NUMBER_ONE) - { - *num_p = ecma_number_make_nan (); - } - else if ((ecma_number_is_negative (y) && x_abs < ECMA_NUMBER_ONE) - || (!ecma_number_is_negative (y) && x_abs > ECMA_NUMBER_ONE)) - { - *num_p = ecma_number_make_infinity (false); - } - else - { - JERRY_ASSERT ((ecma_number_is_negative (y) && x_abs > ECMA_NUMBER_ONE) - || (!ecma_number_is_negative (y) && x_abs < ECMA_NUMBER_ONE)); - - *num_p = ECMA_NUMBER_ZERO; - } - } - else - { - const ecma_number_t diff_is_int = ecma_op_number_remainder (y, ECMA_NUMBER_ONE); - const ecma_number_t rel_diff_is_int = ecma_number_abs (ecma_number_divide (diff_is_int, - y)); - const ecma_number_t y_int = ecma_number_substract (y, diff_is_int); - - const ecma_number_t y_int_half = ecma_number_multiply (y_int, ECMA_NUMBER_HALF); - const ecma_number_t diff_is_odd = ecma_op_number_remainder (y_int_half, ECMA_NUMBER_ONE); - const ecma_number_t rel_diff_is_odd = ecma_number_abs (ecma_number_divide (diff_is_odd, - y_int_half)); - - const bool is_y_int = (rel_diff_is_int < ecma_number_relative_eps); - const bool is_y_odd = (is_y_int && rel_diff_is_odd > ecma_number_relative_eps); - - if (ecma_number_is_infinity (x)) - { - if (!ecma_number_is_negative (x)) - { - if (y > ECMA_NUMBER_ZERO) - { - *num_p = ecma_number_make_infinity (false); - } - else - { - JERRY_ASSERT (y < ECMA_NUMBER_ZERO); - - *num_p = ECMA_NUMBER_ZERO; - } - } - else - { - if (y > ECMA_NUMBER_ZERO) - { - *num_p = ecma_number_make_infinity (is_y_odd); - } - else - { - JERRY_ASSERT (y < ECMA_NUMBER_ZERO); - - if (is_y_odd) - { - *num_p = ecma_number_negate (ECMA_NUMBER_ZERO); - } - else - { - *num_p = ECMA_NUMBER_ZERO; - } - } - } - } - else if (ecma_number_is_zero (x)) - { - if (!ecma_number_is_negative (x)) - { - if (y > ECMA_NUMBER_ZERO) - { - *num_p = ECMA_NUMBER_ZERO; - } - else - { - JERRY_ASSERT (y < ECMA_NUMBER_ZERO); - - *num_p = ecma_number_make_infinity (false); - } - } - else - { - if (y > ECMA_NUMBER_ZERO) - { - if (is_y_odd) - { - *num_p = ecma_number_negate (ECMA_NUMBER_ZERO); - } - else - { - *num_p = ECMA_NUMBER_ZERO; - } - } - else - { - *num_p = ecma_number_make_infinity (is_y_odd); - } - } - } - else if (!ecma_number_is_infinity (x) - && x < ECMA_NUMBER_ZERO - && !ecma_number_is_infinity (y) - && !is_y_int) - { - *num_p = ecma_number_make_nan (); - } - else - { - JERRY_ASSERT (!ecma_number_is_infinity (x) - && !ecma_number_is_zero (x)); - JERRY_ASSERT (!ecma_number_is_infinity (y) - && !ecma_number_is_zero (y)); - - const bool sign = (x < ECMA_NUMBER_ZERO && is_y_odd); - const bool invert = (y < ECMA_NUMBER_ZERO); - - JERRY_ASSERT (is_y_int || !sign); - - ecma_number_t positive_x; - ecma_number_t positive_y; - - if (x < ECMA_NUMBER_ZERO) - { - JERRY_ASSERT (x < ECMA_NUMBER_ZERO); - - positive_x = ecma_number_negate (x); - } - else - { - positive_x = x; - } - - if (invert) - { - positive_y = ecma_number_negate (y); - } - else - { - positive_y = y; - } - - ecma_number_t ret_num; - - if (is_y_int - && ecma_uint32_to_number (ecma_number_to_uint32 (positive_y)) == positive_y) - { - TODO (/* Check for license issues */); - - uint32_t power_uint32 = ecma_number_to_uint32 (positive_y); - - ret_num = ECMA_NUMBER_ONE; - ecma_number_t power_accumulator = positive_x; - - while (power_uint32 != 0) - { - if (power_uint32 % 2) - { - ret_num = ecma_number_multiply (ret_num, power_accumulator); - - power_uint32--; - } - - power_accumulator = ecma_number_multiply (power_accumulator, power_accumulator); - power_uint32 /= 2; - } - } - else - { - /* pow (x, y) = exp (y * ln (x)) */ - ecma_number_t ln_x = ecma_number_ln (positive_x); - ecma_number_t y_m_ln_x = ecma_number_multiply (positive_y, ln_x); - ret_num = ecma_number_exp (y_m_ln_x); - } - - if (sign) - { - ret_num = ecma_number_negate (ret_num); - } - - if (invert) - { - ret_num = ecma_number_divide (ECMA_NUMBER_ONE, ret_num); - } - - *num_p = ret_num; - } - } - + *num_p = DOUBLE_TO_ECMA_NUMBER_T (pow (x, y)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); ECMA_OP_TO_NUMBER_FINALIZE (y); @@ -863,53 +629,10 @@ ecma_builtin_math_object_sin (ecma_value_t this_arg __attr_unused___, /**< 'this ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); ecma_number_t *num_p = ecma_alloc_number (); - - if (ecma_number_is_nan (arg_num) - || ecma_number_is_infinity (arg_num)) - { - *num_p = ecma_number_make_nan (); - } - else if (ecma_number_is_zero (arg_num)) - { - *num_p = arg_num; - } - else - { - /* Taylor series of sin (x) around x = 0 is x - x^3/3! + x^5/5! - x^7/7! + ... */ - - ecma_number_t x = ecma_op_number_remainder (arg_num, 2 * ECMA_NUMBER_PI); - ecma_number_t neg_sqr_x = ecma_number_negate (ecma_number_multiply (x, x)); - - ecma_number_t sum = ECMA_NUMBER_ZERO; - ecma_number_t next_addendum = ecma_number_divide (x, ECMA_NUMBER_ONE); - ecma_number_t next_factorial_factor = ECMA_NUMBER_ONE; - - ecma_number_t diff = ecma_number_make_infinity (false); - - while ((ecma_number_is_zero (sum) && !ecma_number_is_zero (diff)) - || (!ecma_number_is_zero (sum) - && ecma_number_abs (ecma_number_divide (diff, sum)) > ecma_number_relative_eps)) - { - ecma_number_t next_sum = ecma_number_add (sum, next_addendum); - - next_addendum = ecma_number_multiply (next_addendum, neg_sqr_x); - next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE); - next_addendum = ecma_number_divide (next_addendum, next_factorial_factor); - next_factorial_factor = ecma_number_add (next_factorial_factor, ECMA_NUMBER_ONE); - next_addendum = ecma_number_divide (next_addendum, next_factorial_factor); - - diff = ecma_number_abs (ecma_number_substract (sum, next_sum)); - - sum = next_sum; - } - - *num_p = sum; - } - + *num_p = DOUBLE_TO_ECMA_NUMBER_T (sin (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); ECMA_OP_TO_NUMBER_FINALIZE (arg_num); - return ret_value; } /* ecma_builtin_math_object_sin */ @@ -930,36 +653,11 @@ ecma_builtin_math_object_sqrt (ecma_value_t this_arg __attr_unused___, /**< 'thi ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); - ecma_number_t ret_num; - - if (ecma_number_is_nan (arg_num) - || (!ecma_number_is_zero (arg_num) - && ecma_number_is_negative (arg_num))) - { - ret_num = ecma_number_make_nan (); - } - else if (ecma_number_is_zero (arg_num)) - { - ret_num = arg_num; - } - else if (ecma_number_is_infinity (arg_num)) - { - JERRY_ASSERT (!ecma_number_is_negative (arg_num)); - - ret_num = arg_num; - } - else - { - ret_num = ecma_number_sqrt (arg_num); - } - ecma_number_t *num_p = ecma_alloc_number (); - *num_p = ret_num; - + *num_p = DOUBLE_TO_ECMA_NUMBER_T (sqrt (arg_num)); ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); ECMA_OP_TO_NUMBER_FINALIZE (arg_num); - return ret_value; } /* ecma_builtin_math_object_sqrt */ @@ -973,10 +671,20 @@ ecma_builtin_math_object_sqrt (ecma_value_t this_arg __attr_unused___, /**< 'thi * Returned value must be freed with ecma_free_completion_value. */ static ecma_completion_value_t -ecma_builtin_math_object_tan (ecma_value_t this_arg, /**< 'this' argument */ +ecma_builtin_math_object_tan (ecma_value_t this_arg __attr_unused___, /**< 'this' argument */ ecma_value_t arg) /**< routine's argument */ { - ECMA_BUILTIN_CP_UNIMPLEMENTED (this_arg, arg); + ecma_completion_value_t ret_value = ecma_make_empty_completion_value (); + + ECMA_OP_TO_NUMBER_TRY_CATCH (arg_num, arg, ret_value); + + ecma_number_t *num_p = ecma_alloc_number (); + *num_p = DOUBLE_TO_ECMA_NUMBER_T (tan (arg_num)); + + ret_value = ecma_make_normal_completion_value (ecma_make_number_value (num_p)); + + ECMA_OP_TO_NUMBER_FINALIZE (arg_num); + return ret_value; } /* ecma_builtin_math_object_tan */ /** diff --git a/third-party/fdlibm/CMakeLists.txt b/third-party/fdlibm/CMakeLists.txt new file mode 100644 index 0000000000..967d88c813 --- /dev/null +++ b/third-party/fdlibm/CMakeLists.txt @@ -0,0 +1,69 @@ +# Copyright 2015 Samsung Electronics Co., Ltd. +# Copyright 2015 University of Szeged. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +cmake_minimum_required (VERSION 2.8.12) +project (jerry_fdlibm C) + +# Compiler / linker flags +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_JERRY} ${C_FLAGS_JERRY}") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=parentheses") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=sign-compare") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=sign-conversion") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=strict-aliasing") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unknown-pragmas") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=missing-declarations") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=maybe-uninitialized") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unused-but-set-variable") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=unused-variable") +set(COMPILE_FLAGS_FDLIBM "${COMPILE_FLAGS_FDLIBM} -Wno-error=conversion") + +# Include directories +set(INCLUDE_FDLIBM ${CMAKE_SOURCE_DIR}/third-party/fdlibm/include) +set(INCLUDE_FDLIBM ${INCLUDE_FDLIBM} PARENT_SCOPE) + +# Source directories +file(GLOB SOURCE_FDLIBM *.c) + +add_custom_target (jerry-fdlibm-all) + +# Targets declaration + function(declare_targets_for_build_mode BUILD_MODE) + set(TARGET_NAME ${BUILD_MODE_PREFIX_${BUILD_MODE}}) + + function(declare_target_with_modifiers ) # modifiers are passed in ARGN implicit argument + foreach(MODIFIER ${ARGN}) + set(TARGET_NAME ${TARGET_NAME}${MODIFIER_SUFFIX_${MODIFIER}}) + endforeach() + + add_library(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} STATIC ${SOURCE_FDLIBM}) + set_property(TARGET ${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} + PROPERTY COMPILE_FLAGS "${COMPILE_FLAGS_FDLIBM}") + target_include_directories(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} PRIVATE ${INCLUDE_FDLIBM}) + + if("${BUILD_MODE}" STREQUAL "UNITTESTS") + target_include_directories(${TARGET_NAME}.jerry-fdlibm.${SUFFIX_THIRD_PARTY_LIB} INTERFACE ${INCLUDE_FDLIBM}) + endif() + endfunction() + + foreach(MODIFIERS_LIST ${MODIFIERS_LISTS}) + separate_arguments(MODIFIERS_LIST) + + declare_target_with_modifiers(${MODIFIERS_LIST}) + endforeach() + endfunction() + + declare_targets_for_build_mode(DEBUG) + declare_targets_for_build_mode(RELEASE) + declare_targets_for_build_mode(UNITTESTS) \ No newline at end of file diff --git a/third-party/fdlibm/e_acos.c b/third-party/fdlibm/e_acos.c new file mode 100644 index 0000000000..d7c9ed2258 --- /dev/null +++ b/third-party/fdlibm/e_acos.c @@ -0,0 +1,105 @@ + +/* @(#)e_acos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: sqrt + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_acos(double x) +#else + double __ieee754_acos(x) + double x; +#endif +{ + double z,p,q,r,w,s,c,df; + int hx,ix; + hx = __HI(x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + if(((ix-0x3ff00000)|__LO(x))==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = sqrt(z); + df = s; + __LO(df) = 0; + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/third-party/fdlibm/e_asin.c b/third-party/fdlibm/e_asin.c new file mode 100644 index 0000000000..1d503fc22e --- /dev/null +++ b/third-party/fdlibm/e_asin.c @@ -0,0 +1,114 @@ + +/* @(#)e_asin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +#ifdef __STDC__ + double __ieee754_asin(double x) +#else + double __ieee754_asin(x) + double x; +#endif +{ + double t = 0,w,p,q,c,r,s; + int hx,ix; + hx = __HI(x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + if(((ix-0x3ff00000)|__LO(x))==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + __LO(w) = 0; + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/third-party/fdlibm/e_atan2.c b/third-party/fdlibm/e_atan2.c new file mode 100644 index 0000000000..4e731baa32 --- /dev/null +++ b/third-party/fdlibm/e_atan2.c @@ -0,0 +1,123 @@ + +/* @(#)e_atan2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +#ifdef __STDC__ + double __ieee754_atan2(double y, double x) +#else + double __ieee754_atan2(y,x) + double y,x; +#endif +{ + double z; + int k,m,hx,hy,ix,iy; + unsigned lx,ly; + + hx = __HI(x); ix = hx&0x7fffffff; + lx = __LO(x); + hy = __HI(y); iy = hy&0x7fffffff; + ly = __LO(y); + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if((hx-0x3ff00000|lx)==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: __HI(z) ^= 0x80000000; + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/third-party/fdlibm/e_exp.c b/third-party/fdlibm/e_exp.c new file mode 100644 index 0000000000..a2554c56d9 --- /dev/null +++ b/third-party/fdlibm/e_exp.c @@ -0,0 +1,156 @@ + +/* @(#)e_exp.c 1.6 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Remes algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+300, +twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + + +#ifdef __STDC__ + double __ieee754_exp(double x) /* default IEEE double exp */ +#else + double __ieee754_exp(x) /* default IEEE double exp */ + double x; +#endif +{ + double y,hi,lo,c,t; + int k = 0,xsb; + unsigned hx; + + hx = __HI(x); /* high word of x */ + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + if(((hx&0xfffff)|__LO(x))!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = (int)(invln2*x+halF[xsb]); + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + __HI(y) += (k<<20); /* add k to y's exponent */ + return y; + } else { + __HI(y) += ((k+1000)<<20);/* add k to y's exponent */ + return y*twom1000; + } +} diff --git a/third-party/fdlibm/e_log.c b/third-party/fdlibm/e_log.c new file mode 100644 index 0000000000..3798bc8027 --- /dev/null +++ b/third-party/fdlibm/e_log.c @@ -0,0 +1,139 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static double zero = 0.0; + +#ifdef __STDC__ + double __ieee754_log(double x) +#else + double __ieee754_log(x) + double x; +#endif +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int k,hx,i,j; + unsigned lx; + + hx = __HI(x); /* high word of x */ + lx = __LO(x); /* low word of x */ + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + hx = __HI(x); /* high word of x */ + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + __HI(x) = hx|(i^0x3ff00000); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/third-party/fdlibm/e_pow.c b/third-party/fdlibm/e_pow.c new file mode 100644 index 0000000000..5683bf5fd8 --- /dev/null +++ b/third-party/fdlibm/e_pow.c @@ -0,0 +1,309 @@ + +#ifndef lint +static char sccsid[] = "@(#)e_pow.c 1.5 04/04/22 SMI"; +#endif + +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating muti-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +#ifdef __STDC__ + double __ieee754_pow(double x, double y) +#else + double __ieee754_pow(x,y) + double x, y; +#endif +{ + double z,ax,z_h,z_l,p_h,p_l; + double y1,t1,t2,r,s,t,u,v,w; + int i0,i1,i,j,k,yisint,n; + int hx,hy,ix,iy; + unsigned lx,ly; + + i0 = ((*(int*)&one)>>29)^1; i1=1-i0; + hx = __HI(x); lx = __LO(x); + hy = __HI(y); ly = __LO(y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return y - y; /* inf**+-1 is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + n = (hx>>31)+1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + __LO(t1) = 0; + t2 = v-(t1-u); + } else { + double ss,s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; ix = __HI(ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = ss*ss; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+ss); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + __LO(t_h) = 0; + t_l = r-((t_h-3.0)-s2); + /* u+v = ss*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*ss; + /* 2/(3log2)*(ss+...) */ + p_h = u+v; + __LO(p_h) = 0; + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + __LO(t1) = 0; + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into y1+y2 and compute (y1+y2)*(t1+t2) */ + y1 = y; + __LO(y1) = 0; + p_l = (y-y1)*t1+y*t2; + p_h = y1*t1; + z = p_l+p_h; + j = __HI(z); + i = __LO(z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + __HI(t) = (n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + __LO(t) = 0; + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + j = __HI(z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else __HI(z) += (n<<20); + return s*z; +} diff --git a/third-party/fdlibm/e_rem_pio2.c b/third-party/fdlibm/e_rem_pio2.c new file mode 100644 index 0000000000..7242bb232b --- /dev/null +++ b/third-party/fdlibm/e_rem_pio2.c @@ -0,0 +1,175 @@ + +/* @(#)e_rem_pio2.c 1.4 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include "fdlibm.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +#ifdef __STDC__ +static const int two_over_pi[] = { +#else +static int two_over_pi[] = { +#endif +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +#ifdef __STDC__ +static const int npio2_hw[] = { +#else +static int npio2_hw[] = { +#endif +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +#ifdef __STDC__ + int __ieee754_rem_pio2(double x, double *y) +#else + int __ieee754_rem_pio2(x,y) + double x,y[]; +#endif +{ + double z,w,t,r,fn; + double tx[3]; + int e0,i,j,nx,n,ix,hx; + + hx = __HI(x); /* high word of x */ + ix = hx&0x7fffffff; + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int) (t*invpio2+half); + fn = (double)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + if(n<32&&ix!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + j = ix>>20; + y[0] = r-w; + i = j-(((__HI(y[0]))>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + i = j-(((__HI(y[0]))>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + __LO(z) = __LO(x); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + __HI(z) = ix - (e0<<20); + for(i=0;i<2;i++) { + tx[i] = (double)((int)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/third-party/fdlibm/e_sqrt.c b/third-party/fdlibm/e_sqrt.c new file mode 100644 index 0000000000..ba49f649b2 --- /dev/null +++ b/third-party/fdlibm/e_sqrt.c @@ -0,0 +1,450 @@ +/* @(#)e_sqrt.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __ieee754_sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebric manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double one = 1.0, tiny=1.0e-300; +#else +static double one = 1.0, tiny=1.0e-300; +#endif + +#ifdef __STDC__ + double __ieee754_sqrt(double x) +#else + double __ieee754_sqrt(x) + double x; +#endif +{ + double z; + int sign = (int)0x80000000; + unsigned r,t1,s1,ix1,q1; + int ix0,s0,q,m,t,i; + + ix0 = __HI(x); /* high word of x */ + ix1 = __LO(x); /* low word of x */ + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(unsigned)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(unsigned)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + __HI(z) = ix0; + __LO(z) = ix1; + return z; +} + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper then the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ + diff --git a/third-party/fdlibm/include/fdlibm-math.h b/third-party/fdlibm/include/fdlibm-math.h new file mode 100644 index 0000000000..999e067a53 --- /dev/null +++ b/third-party/fdlibm/include/fdlibm-math.h @@ -0,0 +1,79 @@ +/* Copyright 2014-2015 Samsung Electronics Co., Ltd. + * Copyright 2015 University of Szeged. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. + */ + +#ifndef JERRY_FDLIBM_MATH_H +#define JERRY_FDLIBM_MATH_H + +#ifdef __cplusplus +# define EXTERN_C "C" +#else /* !__cplusplus */ +# define EXTERN_C +#endif /* !__cplusplus */ + +// General Constants + +#define INFINITY (1.0/0.0) +#define NAN (0.0/0.0) +#define HUGE_VAL INFINITY + +#define isnan(x) ((x) != (x)) +#define isinf(x) (((x) == INFINITY) || ((x) == -INFINITY)) +#define isfinite(x) (!(isinf(x)) && (x != NAN)) + +// Exponential and Logarithmic constants + +#define M_E 2.7182818284590452353602874713526625 +#define M_SQRT2 1.4142135623730950488016887242096981 +#define M_SQRT1_2 0.7071067811865475244008443621048490 +#define M_LOG2E 1.4426950408889634073599246810018921 +#define M_LOG10E 0.4342944819032518276511289189166051 +#define M_LN2 0.6931471805599453094172321214581765 +#define M_LN10 2.3025850929940456840179914546843642 + +// Trigonometric Constants + +#define M_PI 3.1415926535897932384626433832795029 +#define M_PI_2 1.5707963267948966192313216916397514 +#define M_PI_4 0.7853981633974483096156608458198757 +#define M_1_PI 0.3183098861837906715377675267450287 +#define M_2_PI 0.6366197723675813430755350534900574 +#define M_2_SQRTPI 1.1283791670955125738961589031215452 + +// Trigonometric functions +extern EXTERN_C double cos(double); +extern EXTERN_C double sin(double); +extern EXTERN_C double tan(double); +extern EXTERN_C double acos(double); +extern EXTERN_C double asin(double); +extern EXTERN_C double atan(double); +extern EXTERN_C double atan2(double, double); + +// Exponential and logarithmic functions +extern EXTERN_C double exp(double); +extern EXTERN_C double log(double); + +// Power functions +extern EXTERN_C double pow(double, double); +extern EXTERN_C double sqrt(double); + +// Rounding and remainder functions +extern EXTERN_C double ceil(double); +extern EXTERN_C double floor(double); + +// Other functions +extern EXTERN_C double fabs(double); + +#endif /* !JERRY_FDLIBM_MATH_H */ diff --git a/third-party/fdlibm/include/fdlibm.h b/third-party/fdlibm/include/fdlibm.h new file mode 100644 index 0000000000..817f22a8cd --- /dev/null +++ b/third-party/fdlibm/include/fdlibm.h @@ -0,0 +1,217 @@ + +/* @(#)fdlibm.h 1.5 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Sometimes it's necessary to define __LITTLE_ENDIAN explicitly + but these catch some common cases. */ + +#if defined(i386) || defined(i486) || \ + defined(intel) || defined(x86) || defined(i86pc) || \ + defined(__alpha) || defined(__osf__) || \ + defined(__x86_64__) || defined(__arm__) +#define __LITTLE_ENDIAN +#endif + +#ifdef __LITTLE_ENDIAN +#define __HI(x) *(1+(int*)&x) +#define __LO(x) *(int*)&x +#define __HIp(x) *(1+(int*)x) +#define __LOp(x) *(int*)x +#else +#define __HI(x) *(int*)&x +#define __LO(x) *(1+(int*)&x) +#define __HIp(x) *(int*)x +#define __LOp(x) *(1+(int*)x) +#endif + +#ifdef __STDC__ +#define __P(p) p +#else +#define __P(p) () +#endif + +/* + * ANSI/POSIX + */ + +extern int signgam; + +#define MAXFLOAT ((float)3.40282346638528860e+38) + +enum fdversion {fdlibm_ieee = -1, fdlibm_svid, fdlibm_xopen, fdlibm_posix}; + +#define _LIB_VERSION_TYPE enum fdversion +#define _LIB_VERSION _fdlib_version + +/* if global variable _LIB_VERSION is not desirable, one may + * change the following to be a constant by: + * #define _LIB_VERSION_TYPE const enum version + * In that case, after one initializes the value _LIB_VERSION (see + * s_lib_version.c) during compile time, it cannot be modified + * in the middle of a program + */ +extern _LIB_VERSION_TYPE _LIB_VERSION; + +#define _IEEE_ fdlibm_ieee +#define _SVID_ fdlibm_svid +#define _XOPEN_ fdlibm_xopen +#define _POSIX_ fdlibm_posix + +struct exception { + int type; + char *name; + double arg1; + double arg2; + double retval; +}; + +#define HUGE MAXFLOAT + +/* + * set X_TLOSS = pi*2**52, which is possibly defined in + * (one may replace the following line by "#include ") + */ + +#define X_TLOSS 1.41484755040568800000e+16 + +#define DOMAIN 1 +#define SING 2 +#define OVERFLOW 3 +#define UNDERFLOW 4 +#define TLOSS 5 +#define PLOSS 6 + +/* + * ANSI/POSIX + */ +extern double acos __P((double)); +extern double asin __P((double)); +extern double atan __P((double)); +extern double atan2 __P((double, double)); +extern double cos __P((double)); +extern double sin __P((double)); +extern double tan __P((double)); + +extern double cosh __P((double)); +extern double sinh __P((double)); +extern double tanh __P((double)); + +extern double exp __P((double)); +extern double frexp __P((double, int *)); +extern double ldexp __P((double, int)); +extern double log __P((double)); +extern double log10 __P((double)); +extern double modf __P((double, double *)); + +extern double pow __P((double, double)); +extern double sqrt __P((double)); + +extern double ceil __P((double)); +extern double fabs __P((double)); +extern double floor __P((double)); +extern double fmod __P((double, double)); + +extern double erf __P((double)); +extern double erfc __P((double)); +extern double gamma __P((double)); +extern double hypot __P((double, double)); +extern int isnan __P((double)); +extern int finite __P((double)); +extern double j0 __P((double)); +extern double j1 __P((double)); +extern double jn __P((int, double)); +extern double lgamma __P((double)); +extern double y0 __P((double)); +extern double y1 __P((double)); +extern double yn __P((int, double)); + +extern double acosh __P((double)); +extern double asinh __P((double)); +extern double atanh __P((double)); +extern double cbrt __P((double)); +extern double logb __P((double)); +extern double nextafter __P((double, double)); +extern double remainder __P((double, double)); +#ifdef _SCALB_INT +extern double scalb __P((double, int)); +#else +extern double scalb __P((double, double)); +#endif + +extern int matherr __P((struct exception *)); + +/* + * IEEE Test Vector + */ +extern double significand __P((double)); + +/* + * Functions callable from C, intended to support IEEE arithmetic. + */ +extern double copysign __P((double, double)); +extern int ilogb __P((double)); +extern double rint __P((double)); +extern double scalbn __P((double, int)); + +/* + * BSD math library entry points + */ +extern double expm1 __P((double)); +extern double log1p __P((double)); + +/* + * Reentrant version of gamma & lgamma; passes signgam back by reference + * as the second argument; user must allocate space for signgam. + */ +#ifdef _REENTRANT +extern double gamma_r __P((double, int *)); +extern double lgamma_r __P((double, int *)); +#endif /* _REENTRANT */ + +/* ieee style elementary functions */ +extern double __ieee754_sqrt __P((double)); +extern double __ieee754_acos __P((double)); +extern double __ieee754_acosh __P((double)); +extern double __ieee754_log __P((double)); +extern double __ieee754_atanh __P((double)); +extern double __ieee754_asin __P((double)); +extern double __ieee754_atan2 __P((double,double)); +extern double __ieee754_exp __P((double)); +extern double __ieee754_cosh __P((double)); +extern double __ieee754_fmod __P((double,double)); +extern double __ieee754_pow __P((double,double)); +extern double __ieee754_lgamma_r __P((double,int *)); +extern double __ieee754_gamma_r __P((double,int *)); +extern double __ieee754_lgamma __P((double)); +extern double __ieee754_gamma __P((double)); +extern double __ieee754_log10 __P((double)); +extern double __ieee754_sinh __P((double)); +extern double __ieee754_hypot __P((double,double)); +extern double __ieee754_j0 __P((double)); +extern double __ieee754_j1 __P((double)); +extern double __ieee754_y0 __P((double)); +extern double __ieee754_y1 __P((double)); +extern double __ieee754_jn __P((int,double)); +extern double __ieee754_yn __P((int,double)); +extern double __ieee754_remainder __P((double,double)); +extern int __ieee754_rem_pio2 __P((double,double*)); +#ifdef _SCALB_INT +extern double __ieee754_scalb __P((double,int)); +#else +extern double __ieee754_scalb __P((double,double)); +#endif + +/* fdlibm kernel function */ +extern double __kernel_standard __P((double,double,int)); +extern double __kernel_sin __P((double,double,int)); +extern double __kernel_cos __P((double,double)); +extern double __kernel_tan __P((double,double,int)); +extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*)); diff --git a/third-party/fdlibm/k_cos.c b/third-party/fdlibm/k_cos.c new file mode 100644 index 0000000000..7fb855d25e --- /dev/null +++ b/third-party/fdlibm/k_cos.c @@ -0,0 +1,92 @@ + +/* @(#)k_cos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +#ifdef __STDC__ + double __kernel_cos(double x, double y) +#else + double __kernel_cos(x, y) + double x,y; +#endif +{ + double a,hz,z,r,qx; + int ix; + ix = __HI(x)&0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + __HI(qx) = ix-0x00200000; /* x/4 */ + __LO(qx) = 0; + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/third-party/fdlibm/k_rem_pio2.c b/third-party/fdlibm/k_rem_pio2.c new file mode 100644 index 0000000000..ec473ac0d3 --- /dev/null +++ b/third-party/fdlibm/k_rem_pio2.c @@ -0,0 +1,316 @@ + +/* @(#)k_rem_pio2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] ouput result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ +#else +static int init_jk[] = {2,3,4,6}; +#endif + +#ifdef __STDC__ +static const double PIo2[] = { +#else +static double PIo2[] = { +#endif + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +#ifdef __STDC__ +static const double +#else +static double +#endif +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +#ifdef __STDC__ + int __kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int *ipio2) +#else + int __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + double x[], y[]; int e0,nx,prec; int ipio2[]; +#endif +{ + int jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int)(twon24* z)); + iq[i] = (int)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int)(twon24*z)); + iq[jz] = (int)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int) fw; + } else iq[jz] = (int) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/third-party/fdlibm/k_sin.c b/third-party/fdlibm/k_sin.c new file mode 100644 index 0000000000..dfcad764ed --- /dev/null +++ b/third-party/fdlibm/k_sin.c @@ -0,0 +1,74 @@ + +/* @(#)k_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +#ifdef __STDC__ + double __kernel_sin(double x, double y, int iy) +#else + double __kernel_sin(x, y, iy) + double x,y; int iy; /* iy=0 if y is zero */ +#endif +{ + double z,r,v; + int ix; + ix = __HI(x)&0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/third-party/fdlibm/k_standard.c b/third-party/fdlibm/k_standard.c new file mode 100644 index 0000000000..d6e4a82ec4 --- /dev/null +++ b/third-party/fdlibm/k_standard.c @@ -0,0 +1,733 @@ + +/* @(#)k_standard.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include "fdlibm.h" +#include + +#ifndef _USE_WRITE +#include /* fputs(), stderr */ +// #define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include /* write */ +// #define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +static double zero = 0.0; /* used as const */ + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 20-- pow(0.0,0.0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- gamma(finite) overflow + * 41-- gamma(-integer) + * 42-- pow(NaN,0.0) + */ + + +#ifdef __STDC__ + double __kernel_standard(double x, double y, int type) +#else + double __kernel_standard(x,y,type) + double x,y; int type; +#endif +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + __HI(inf) = 0x7ff00000; /* set inf to infinite */ +#endif + +#ifdef _USE_WRITE + (void) fflush(stdout); +#endif + exc.arg1 = x; + exc.arg2 = y; + switch(type) { + case 1: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = "acos"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if(_LIB_VERSION == _SVID_) { + // // (void) WRITE2("acos: DOMAIN error\n", 19); + // } + // errno = EDOM; + // } + break; + case 2: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = "asin"; + exc.retval = zero; + // if(_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if(_LIB_VERSION == _SVID_) { + // // (void) WRITE2("asin: DOMAIN error\n", 19); + // } + // errno = EDOM; + // } + break; + case 3: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = "atan2"; + exc.retval = zero; + // if(_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if(_LIB_VERSION == _SVID_) { + // // (void) WRITE2("atan2: DOMAIN error\n", 20); + // } + // errno = EDOM; + // } + break; + case 4: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = "hypot"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 5: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = "cosh"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 6: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = "exp"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 7: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = "exp"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 8: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "y0"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("y0: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 9: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = "y0"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("y0: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 10: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "y1"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("y1: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 11: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = "y1"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("y1: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 12: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = "yn"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("yn: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 13: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = "yn"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("yn: DOMAIN error\n", 17); + // } + // errno = EDOM; + // } + break; + case 14: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = "lgamma"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 15: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = "lgamma"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("lgamma: SING error\n", 19); + // } + // errno = EDOM; + // } + break; + case 16: + /* log(0) */ + exc.type = SING; + exc.name = "log"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("log: SING error\n", 16); + // } + // errno = EDOM; + // } + break; + case 17: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = "log"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("log: DOMAIN error\n", 18); + // } + // errno = EDOM; + // } + break; + case 18: + /* log10(0) */ + exc.type = SING; + exc.name = "log10"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("log10: SING error\n", 18); + // } + // errno = EDOM; + // } + break; + case 19: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = "log10"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("log10: DOMAIN error\n", 20); + // } + // errno = EDOM; + // } + break; + case 20: + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.retval = zero; + // if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + // else if (!matherr(&exc)) { + // // (void) WRITE2("pow(0,0): DOMAIN error\n", 23); + // errno = EDOM; + // } + break; + case 21: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = "pow"; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(xzero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 26: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = "sqrt"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("sqrt: DOMAIN error\n", 19); + // } + // errno = EDOM; + // } + break; + case 27: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = "fmod"; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("fmod: DOMAIN error\n", 20); + // } + // errno = EDOM; + // } + break; + case 28: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = "remainder"; + exc.retval = zero/zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("remainder: DOMAIN error\n", 24); + // } + // errno = EDOM; + // } + break; + case 29: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = "acosh"; + exc.retval = zero/zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("acosh: DOMAIN error\n", 20); + // } + // errno = EDOM; + // } + break; + case 30: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = "atanh"; + exc.retval = zero/zero; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("atanh: DOMAIN error\n", 20); + // } + // errno = EDOM; + // } + break; + case 31: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = "atanh"; + exc.retval = x/zero; /* sign(x)*inf */ + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("atanh: SING error\n", 18); + // } + // errno = EDOM; + // } + break; + case 32: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = "scalb"; + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 33: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = "scalb"; + exc.retval = copysign(zero,x); + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 34: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j0"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 35: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y0"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 36: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "j1"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 37: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "y1"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 38: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "jn"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 39: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = "yn"; + exc.retval = zero; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2(exc.name, 2); + // // (void) WRITE2(": TLOSS error\n", 14); + // } + // errno = ERANGE; + // } + break; + case 40: + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = "gamma"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = ERANGE; + // else if (!matherr(&exc)) { + // errno = ERANGE; + // } + break; + case 41: + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + exc.name = "gamma"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + // if (_LIB_VERSION == _POSIX_) + // errno = EDOM; + // else if (!matherr(&exc)) { + // if (_LIB_VERSION == _SVID_) { + // // (void) WRITE2("gamma: SING error\n", 18); + // } + // errno = EDOM; + // } + break; + case 42: + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = "pow"; + exc.retval = x; + // if (_LIB_VERSION == _IEEE_ || + // _LIB_VERSION == _POSIX_) exc.retval = 1.0; + // else if (!matherr(&exc)) { + // errno = EDOM; + // } + // break; + } + return exc.retval; +} diff --git a/third-party/fdlibm/k_tan.c b/third-party/fdlibm/k_tan.c new file mode 100644 index 0000000000..017c1e57c1 --- /dev/null +++ b/third-party/fdlibm/k_tan.c @@ -0,0 +1,148 @@ +#pragma ident "@(#)k_tan.c 1.5 04/04/22 SMI" + +/* + * ==================================================== + * Copyright 2004 Sun Microsystems, Inc. All Rights Reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* INDENT OFF */ +/* __kernel_tan( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k = 1) or -1/tan (if k = -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include "fdlibm.h" + +static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ + 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ + 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ + 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ + 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ + 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ + -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ + 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ +/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ +}; +#define one xxx[13] +#define pio4 xxx[14] +#define pio4lo xxx[15] +#define T xxx +/* INDENT ON */ + +double +__kernel_tan(double x, double y, int iy) { + double z, r, v, w, s; + int ix, hx; + + hx = __HI(x); /* high word of x */ + ix = hx & 0x7fffffff; /* high word of |x| */ + if (ix < 0x3e300000) { /* x < 2**-28 */ + if ((int) x == 0) { /* generate inexact */ + if (((ix | __LO(x)) | (iy + 1)) == 0) + return one / fabs(x); + else { + if (iy == 1) + return x; + else { /* compute -1 / (x+y) carefully */ + double a, t; + + z = w = x + y; + __LO(z) = 0; + v = y - (z - x); + t = a = -one / w; + __LO(t) = 0; + s = one + t * z; + return t + a * (s + t * v); + } + } + } + } + if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ + if (hx < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + w = z * z; + /* + * Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + + w * T[11])))); + v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + + w * T[12]))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T[0] * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = (double) iy; + return (double) (1 - ((hx >> 30) & 2)) * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + double a, t; + z = w; + __LO(z) = 0; + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + __LO(t) = 0; + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/third-party/fdlibm/s_atan.c b/third-party/fdlibm/s_atan.c new file mode 100644 index 0000000000..0093eafdfd --- /dev/null +++ b/third-party/fdlibm/s_atan.c @@ -0,0 +1,134 @@ + +/* @(#)s_atan.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double atanhi[] = { +#else +static double atanhi[] = { +#endif + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +#ifdef __STDC__ +static const double atanlo[] = { +#else +static double atanlo[] = { +#endif + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +#ifdef __STDC__ +static const double aT[] = { +#else +static double aT[] = { +#endif + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + +#ifdef __STDC__ + static const double +#else + static double +#endif +one = 1.0, +huge = 1.0e300; + +#ifdef __STDC__ + double atan(double x) +#else + double atan(x) + double x; +#endif +{ + double w,s1,s2,z; + int ix,hx,id; + + hx = __HI(x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(__LO(x)!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/third-party/fdlibm/s_ceil.c b/third-party/fdlibm/s_ceil.c new file mode 100644 index 0000000000..af74592ed2 --- /dev/null +++ b/third-party/fdlibm/s_ceil.c @@ -0,0 +1,78 @@ + +/* @(#)s_ceil.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double ceil(double x) +#else + double ceil(x) + double x; +#endif +{ + int i0,i1,j0; + unsigned i,j; + i0 = __HI(x); + i1 = __LO(x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((unsigned)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(j0==20) i0+=1; + else { + j = i1 + (1<<(52-j0)); + if(j=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} diff --git a/third-party/fdlibm/s_fabs.c b/third-party/fdlibm/s_fabs.c new file mode 100644 index 0000000000..0c4dd64361 --- /dev/null +++ b/third-party/fdlibm/s_fabs.c @@ -0,0 +1,29 @@ + +/* @(#)s_fabs.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * fabs(x) returns the absolute value of x. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double fabs(double x) +#else + double fabs(x) + double x; +#endif +{ + __HI(x) &= 0x7fffffff; + return x; +} diff --git a/third-party/fdlibm/s_finite.c b/third-party/fdlibm/s_finite.c new file mode 100644 index 0000000000..42e1728d7e --- /dev/null +++ b/third-party/fdlibm/s_finite.c @@ -0,0 +1,31 @@ + +/* @(#)s_finite.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + int finite(double x) +#else + int finite(x) + double x; +#endif +{ + int hx; + hx = __HI(x); + return (unsigned)((hx&0x7fffffff)-0x7ff00000)>>31; +} diff --git a/third-party/fdlibm/s_floor.c b/third-party/fdlibm/s_floor.c new file mode 100644 index 0000000000..b37c41ba40 --- /dev/null +++ b/third-party/fdlibm/s_floor.c @@ -0,0 +1,79 @@ + +/* @(#)s_floor.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double huge = 1.0e300; +#else +static double huge = 1.0e300; +#endif + +#ifdef __STDC__ + double floor(double x) +#else + double floor(x) + double x; +#endif +{ + int i0,i1,j0; + unsigned i,j; + i0 = __HI(x); + i1 = __LO(x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>j0; + i0 &= (~i); i1=0; + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((unsigned)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(j0==20) i0+=1; + else { + j = i1+(1<<(52-j0)); + if(j>31; + hx = 0x7ff00000 - hx; + return ((unsigned)(hx))>>31; +} diff --git a/third-party/fdlibm/s_lib_version.c b/third-party/fdlibm/s_lib_version.c new file mode 100644 index 0000000000..40f065e502 --- /dev/null +++ b/third-party/fdlibm/s_lib_version.c @@ -0,0 +1,35 @@ + +/* @(#)s_lib_version.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * MACRO for standards + */ + +#include "fdlibm.h" + +/* + * define and initialize _LIB_VERSION + */ +#ifdef _POSIX_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_; +#else +#ifdef _XOPEN_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_; +#else +#ifdef _SVID3_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _SVID_; +#else /* default _IEEE_MODE */ +_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_; +#endif +#endif +#endif diff --git a/third-party/fdlibm/s_rint.c b/third-party/fdlibm/s_rint.c new file mode 100644 index 0000000000..3095e0d385 --- /dev/null +++ b/third-party/fdlibm/s_rint.c @@ -0,0 +1,84 @@ + +/* @(#)s_rint.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +#ifdef __STDC__ + double rint(double x) +#else + double rint(x) + double x; +#endif +{ + int i0,j0,sx; + unsigned i,i1; + double w,t; + i0 = __HI(x); + sx = (i0>>31)&1; + i1 = __LO(x); + j0 = ((i0>>20)&0x7ff)-0x3ff; + if(j0<20) { + if(j0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + __HI(x)=i0; + w = TWO52[sx]+x; + t = w-TWO52[sx]; + i0 = __HI(t); + __HI(t) = (i0&0x7fffffff)|(sx<<31); + return t; + } else { + i = (0x000fffff)>>j0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(j0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>j0); + } + } + } else if (j0>51) { + if(j0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((unsigned)(0xffffffff))>>(j0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(j0-20)); + } + __HI(x) = i0; + __LO(x) = i1; + w = TWO52[sx]+x; + return w-TWO52[sx]; +} diff --git a/third-party/fdlibm/s_scalbn.c b/third-party/fdlibm/s_scalbn.c new file mode 100644 index 0000000000..329be8b896 --- /dev/null +++ b/third-party/fdlibm/s_scalbn.c @@ -0,0 +1,63 @@ + +/* @(#)s_scalbn.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +#ifdef __STDC__ + double scalbn (double x, int n) +#else + double scalbn (x,n) + double x; int n; +#endif +{ + int k,hx,lx; + hx = __HI(x); + lx = __LO(x); + k = (hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + hx = __HI(x); + k = ((hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {__HI(x) = (hx&0x800fffff)|(k<<20); return x;} + if (k <= -54) + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + k += 54; /* subnormal result */ + __HI(x) = (hx&0x800fffff)|(k<<20); + return x*twom54; +} diff --git a/third-party/fdlibm/s_significand.c b/third-party/fdlibm/s_significand.c new file mode 100644 index 0000000000..1a2163671d --- /dev/null +++ b/third-party/fdlibm/s_significand.c @@ -0,0 +1,30 @@ + +/* @(#)s_significand.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * significand(x) computes just + * scalb(x, (double) -ilogb(x)), + * for exercising the fraction-part(F) IEEE 754-1985 test vector. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double significand(double x) +#else + double significand(x) + double x; +#endif +{ + return __ieee754_scalb(x,(double) -ilogb(x)); +} diff --git a/third-party/fdlibm/s_sin.c b/third-party/fdlibm/s_sin.c new file mode 100644 index 0000000000..43394e577c --- /dev/null +++ b/third-party/fdlibm/s_sin.c @@ -0,0 +1,78 @@ + +/* @(#)s_sin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double sin(double x) +#else + double sin(x) + double x; +#endif +{ + double y[2],z=0.0; + int n, ix; + + /* High word of x. */ + ix = __HI(x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} diff --git a/third-party/fdlibm/s_tan.c b/third-party/fdlibm/s_tan.c new file mode 100644 index 0000000000..1f5564bce3 --- /dev/null +++ b/third-party/fdlibm/s_tan.c @@ -0,0 +1,72 @@ + +/* @(#)s_tan.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double tan(double x) +#else + double tan(x) + double x; +#endif +{ + double y[2],z=0.0; + int n, ix; + + /* High word of x. */ + ix = __HI(x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/third-party/fdlibm/s_tanh.c b/third-party/fdlibm/s_tanh.c new file mode 100644 index 0000000000..7d77c2eacf --- /dev/null +++ b/third-party/fdlibm/s_tanh.c @@ -0,0 +1,82 @@ + +/* @(#)s_tanh.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double one=1.0, two=2.0, tiny = 1.0e-300; +#else +static double one=1.0, two=2.0, tiny = 1.0e-300; +#endif + +#ifdef __STDC__ + double tanh(double x) +#else + double tanh(x) + double x; +#endif +{ + double t,z; + int jx,ix; + + /* High word of |x|. */ + jx = __HI(x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/third-party/fdlibm/w_acos.c b/third-party/fdlibm/w_acos.c new file mode 100644 index 0000000000..e463eaf9c1 --- /dev/null +++ b/third-party/fdlibm/w_acos.c @@ -0,0 +1,39 @@ + +/* @(#)w_acos.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * wrap_acos(x) + */ + +#include "fdlibm.h" + + +#ifdef __STDC__ + double acos(double x) /* wrapper acos */ +#else + double acos(x) /* wrapper acos */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_acos(x); +#else + double z; + z = __ieee754_acos(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,1); /* acos(|x|>1) */ + } else + return z; +#endif +} diff --git a/third-party/fdlibm/w_asin.c b/third-party/fdlibm/w_asin.c new file mode 100644 index 0000000000..e8182857c8 --- /dev/null +++ b/third-party/fdlibm/w_asin.c @@ -0,0 +1,41 @@ + +/* @(#)w_asin.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* + * wrapper asin(x) + */ + + +#include "fdlibm.h" + + +#ifdef __STDC__ + double asin(double x) /* wrapper asin */ +#else + double asin(x) /* wrapper asin */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_asin(x); +#else + double z; + z = __ieee754_asin(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,2); /* asin(|x|>1) */ + } else + return z; +#endif +} diff --git a/third-party/fdlibm/w_atan2.c b/third-party/fdlibm/w_atan2.c new file mode 100644 index 0000000000..80ad39b35d --- /dev/null +++ b/third-party/fdlibm/w_atan2.c @@ -0,0 +1,40 @@ + +/* @(#)w_atan2.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +/* + * wrapper atan2(y,x) + */ + +#include "fdlibm.h" + + +#ifdef __STDC__ + double atan2(double y, double x) /* wrapper atan2 */ +#else + double atan2(y,x) /* wrapper atan2 */ + double y,x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2(y,x); +#else + double z; + z = __ieee754_atan2(y,x); + if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z; + if(x==0.0&&y==0.0) { + return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ + } else + return z; +#endif +} diff --git a/third-party/fdlibm/w_exp.c b/third-party/fdlibm/w_exp.c new file mode 100644 index 0000000000..7819ca133c --- /dev/null +++ b/third-party/fdlibm/w_exp.c @@ -0,0 +1,48 @@ + +/* @(#)w_exp.c 1.4 04/04/22 */ +/* + * ==================================================== + * Copyright (C) 2004 by Sun Microsystems, Inc. All rights reserved. + * + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * wrapper exp(x) + */ + +#include "fdlibm.h" + +#ifdef __STDC__ +static const double +#else +static double +#endif +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ + +#ifdef __STDC__ + double exp(double x) /* wrapper exp */ +#else + double exp(x) /* wrapper exp */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_exp(x); +#else + double z; + z = __ieee754_exp(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finite(x)) { + if(x>o_threshold) + return __kernel_standard(x,x,6); /* exp overflow */ + else if(x 0.0) return z; + if(x==0.0) + return __kernel_standard(x,x,16); /* log(0) */ + else + return __kernel_standard(x,x,17); /* log(x<0) */ +#endif +} diff --git a/third-party/fdlibm/w_pow.c b/third-party/fdlibm/w_pow.c new file mode 100644 index 0000000000..850c1162b2 --- /dev/null +++ b/third-party/fdlibm/w_pow.c @@ -0,0 +1,60 @@ + + +/* @(#)w_pow.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * wrapper pow(x,y) return x**y + */ + +#include "fdlibm.h" + + +#ifdef __STDC__ + double pow(double x, double y) /* wrapper pow */ +#else + double pow(x,y) /* wrapper pow */ + double x,y; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_pow(x,y); +#else + double z; + z=__ieee754_pow(x,y); + if(_LIB_VERSION == _IEEE_|| isnan(y)) return z; + if(isnan(x)) { + if(y==0.0) + return __kernel_standard(x,y,42); /* pow(NaN,0.0) */ + else + return z; + } + if(x==0.0){ + if(y==0.0) + return __kernel_standard(x,y,20); /* pow(0.0,0.0) */ + if(finite(y)&&y<0.0) + return __kernel_standard(x,y,23); /* pow(0.0,negative) */ + return z; + } + if(!finite(z)) { + if(finite(x)&&finite(y)) { + if(isnan(z)) + return __kernel_standard(x,y,24); /* pow neg**non-int */ + else + return __kernel_standard(x,y,21); /* pow overflow */ + } + } + if(z==0.0&&finite(x)&&finite(y)) + return __kernel_standard(x,y,22); /* pow underflow */ + return z; +#endif +} diff --git a/third-party/fdlibm/w_sqrt.c b/third-party/fdlibm/w_sqrt.c new file mode 100644 index 0000000000..4dd589e254 --- /dev/null +++ b/third-party/fdlibm/w_sqrt.c @@ -0,0 +1,38 @@ + +/* @(#)w_sqrt.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * wrapper sqrt(x) + */ + +#include "fdlibm.h" + +#ifdef __STDC__ + double sqrt(double x) /* wrapper sqrt */ +#else + double sqrt(x) /* wrapper sqrt */ + double x; +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrt(x); +#else + double z; + z = __ieee754_sqrt(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<0.0) { + return __kernel_standard(x,x,26); /* sqrt(negative) */ + } else + return z; +#endif +} diff --git a/tools/precommit.sh b/tools/precommit.sh index d631ee83c1..8ea3ec15c0 100755 --- a/tools/precommit.sh +++ b/tools/precommit.sh @@ -23,7 +23,7 @@ shift TARGETS="$1" shift -VERA_DIRECTORIES_EXCLUDE_LIST="-path ./third-party -o -path tests" +VERA_DIRECTORIES_EXCLUDE_LIST="-path ./third-party -o -path ./jerry-fdlibm -o -path tests" VERA_CONFIGURATION_PATH="./tools/vera++" SOURCES_AND_HEADERS_LIST=`find . -type d \( $VERA_DIRECTORIES_EXCLUDE_LIST \) -prune -or -name "*.c" -or -name "*.cpp" -or -name "*.h"`